首页
外语
计算机
考研
公务员
职业资格
财经
工程
司法
医学
专升本
自考
实用职业技能
登录
外语
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube tha
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube tha
admin
2022-10-18
63
问题
The surface distance between 2 points on the surface of a cube is the length of the shortest path on the surface of the cube that joins the 2 points.If a cube has edges of length 4 centimeters,what is the surface distance,in centimeters。between the lower left vertex on its front face and the upper right vertex on its back face?
选项
A、
B、
C、
D、
E、
答案
B
解析
The left figure below shows a cube with edge length 4, where P is the lower left vertex on its front face and Q is the upper right vertex on its back face. It is clear that the shortest path on the surface between P and Q consists of a path on the front face joined to a path on the top face, or a path on the front face joined to a path on the right face. In fact, each of these two approaches can be used in essentially the same way to give a path from P to Q, whose length is the surface distance between P and Q. To simplify the exposition, we will consider the case where the surface distance is the length of a certain path P
F
on the front face plus the length of a certain path P
T
on the top face.
The middle figure below shows the top face of the cube lifted about 45 degrees, and the right figure below shows only the front and top faces of the cube after the top face has been lifted 90 degrees. Since rotations of the top face about this "hinge" do not change the length of any path on the front face or on the top face, this rotation by 90 degrees will not change the length of Pp or the length of P
T
and hence this rotation will not change the sum of the lengths of P
F
and P
T
.
In the right figure below, the shortest path from P to Q is the dashed segment shown in the figure. Moreover, the length of this dashed segment is the surface distance between P and Q because if P
F
and P
T
did not correspond to portions of this dashed segment on the front and top faces, respectively, then the sum of the lengths of P
F
and P
T
would be greater than the length of the dashed segment, since the shortest distance between P and Q in the right figure below is the length of the line segment with endpoints P and Q.
From the discussion above, it follows that the surface distance between P and Q is the length of the dashed segment in the right figure, which is easily found by using the Pythagorean
theorem:
The correct answer is B.
转载请注明原文地址:https://kaotiyun.com/show/CktO777K
本试题收录于:
GMAT QUANTITATIVE题库GMAT分类
0
GMAT QUANTITATIVE
GMAT
相关试题推荐
Concerningmoneyoranythingelse,conflictsbetweenhusbandandwifeusuallyreflectapowerstruggle.Conflictsbetweenparent
Steve:Francesca,what’syourfavouritepieceofmusic,wouldyousay?Francesca:Ithinkit’s"PieJesu"byAndrewLloyd-We
WeallknowthatDNAhastheabilitytoidentifyindividualsbut,becauseitisinherited,therearealsoregionsoftheDNAstr
Mancannotgoonincreasinghisnumberatthepresentrate.Inthenext30yearsmanwillfaceaperiodofcrisis.Someexperts
WhatdowemeanbyaperfectEnglishpronunciation?Inone【C1】______therearemanydifferentkindsofEnglishastherearespeak
Whatheis______isneithermoneynorfame,butthesatisfactionofseeinghisstudentsgrowupasbuildersofsocialism.
Iwouldkeepputtingmydreamtothetesteventhoughitmeantlivingwithuncertaintyandfearoffailure.
Inanoldtownlivedamerchant.Heearnedhugeprofitsbyfairmeansandfoul(恶劣的).Withmoreprofitsflowingin,hebecamemor
Whenweplaytenniswehaveto______.Whatisofthegreatestimportancetoafootballteamis______.
Asthepriceofgasolinerises,whichmakessubstitutingalcoholdistilledfromcerealgrainattractive,thepriceofbreadand
随机试题
通用寄存器组的相关有两种解决办法,分别是_______和_______。
《儿女英雄传》的题材类型是()
患者男,84岁。近期出现记忆力下降,静止性震颤,临床诊断为帕金森病。早期,轻症的首先药物为
肛周脓肿常见的后遗症是内痔环切术常有的后遗症是
请简述世亚行对国际竞争性招标(ICB)的审查程序。
《室外排水设计规范》规定,污水管道最小管径为()mm。
19世纪末,维新变法从一种思潮得以发展为一场政治运动,关键是()。
Inthepresenteconomic_______wecanmakeevengreaterprogressthanpreviously.
Demographyisthestatisticalstudyofhumanpopulations.Itcanbeageneralsciencethatcanbeappliedtoanykindof
Ialwayspreferstartingearly,ratherthan(leave)______everythingtothelastminute.
最新回复
(
0
)